IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 40 (2007) R427–R439 doi:10.1088/0022-3727/40/23/R01

TOPICAL REVIEW

Surface texture evolution ofpolycrystalline and nanostructured films:RHEED surface pole figure analysisF Tang, T Parker, G-C Wang and T-M Lu

Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute,110 8th Street, Troy, NY 12180-3590, USA

Received 13 August 2007, in final form 18 September 2007Published 16 November 2007Online at stacks.iop.org/JPhysD/40/R427

AbstractIn this topical review, we outline the construction of a reflection high-energyelectron diffraction (RHEED) surface pole figure from a polycrystalline filmby recording multiple RHEED patterns as the substrate is rotated around thesurface normal. Due to the short penetration depth of electrons, theconstructed pole figure is a surface pole figure. It is in contrast to theconventional x-ray pole figure which gives the average texture informationof the entire polycrystalline film. Examples of the surface pole figureconstruction processes of a fibre texture and a biaxial texture are illustratedusing Ru vertical nanorods and Mg nanoblades, respectively. For a biaxiallytextured film, there often exists an in-plane morphological anisotropy. Thenadditional intensity normalization must be applied to compensate for theeffects of anisotropic morphology on RHEED surface pole figureconstruction. Rich information on the texture evolution, such as the changein the tilt angle of the texture axis, has been obtained from the in situ studyof oblique angle vapour deposition of Mg nanoblades using RHEED surfacepole figures. Finally we make a comparison between the RHEED surfacepole figure and the conventional x-ray pole figure techniques.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The preferred crystalline orientation, or texture, is afundamental property of the polycrystalline film and it directlycontrols many important physical properties such as optical,magnetic, mechanical and electrical properties of the films.Texture formation is a very complex phenomenon. To date,the fundamental understanding of the atomistic mechanismson texture evolution still remains a challenging subject.Many effects such as surface diffusion, step barriers, stickingcoefficient, surface energy, strain energy and shadowing effect[1–6], can play roles in the formation of a texture. To constructa realistic atomistic model, one requires detailed knowledge onhow the surface texture evolves at different stages of growth.This information is very often not available mainly due to the

lack of experimental techniques that allow one to measurethe surface texture quantitatively. The conventional x-raydiffraction (XRD) probes an average texture of the entirethickness of the film since x-ray penetrates into the entirefilm [7]. As the texture of a film very often changes duringgrowth, information on the surface texture evolution is mostlylost in the XRD analysis.

Reflection high-energy electron diffraction (RHEED) hasbeen a powerful technique for the study of surface structureand surface ordering phenomena due to limited penetrationand escape depths of electrons [8]. The electron beam strikesthe surface at a grazing angle of less than a few degrees andthe RHEED pattern is formed on a phosphor screen. Despitemultiple scattering of electrons, RHEED has the advantageof fast data acquisition due to strong electron scattering cross

0022-3727/07/230427+13$30.00 © 2007 IOP Publishing Ltd Printed in the UK R427

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section and is compatible with the deposition of thin filmsin a vacuum. Surface phase, surface reconstruction andcrystallography can be obtained readily from the diffractionpattern. RHEED is also an indispensable tool to monitor layer-by-layer growth of single crystal films. This is achieved byfollowing the ‘intensity oscillation’ phenomenon where eachcycle of oscillation implies the growth of one monolayer ofmaterial [8, 9].

Recent studies showed that RHEED can also be usedto obtain information such as crystal phase, orientationand grain size and shape from the diffraction patterns ofpolycrystalline films [10–17]. However, this RHEED patternonly gives partial information for the crystal orientation.A complete characterization of the texture, including theazimuthal orientation, usually requires the collection ofmultiple diffraction patterns. Brewer et al [18] has used aRHEED in-plane rocking curve to obtain the information aboutthe azimuthal angle orientation of textured thin films. Thisrocking curve is constructed by rotating the sample aroundthe surface normal and recording the maximum intensity foreach diffraction spot. More recently, we demonstrated thefeasibility of a RHEED surface pole figure technique [19,20],by which the complete characterization of the texture becomespossible. In this measurement, the polar angle intensity profileof a particular family of crystal planes is first constructed froma single RHEED pattern. Then the combination of intensityprofiles from multiple RHEED patterns for different azimuthalangles gives a surface pole figure.

In this topical review, we first give a brief overviewof texture characterization by the RHEED pattern analysis.Then the main content of this paper shifts to the newlydeveloped RHEED surface pole figure technique, includingthe construction process and the possible artefacts that canoccur during the combination of multiple RHEED images. Thesurface pole figures of nanostructured films grown by obliqueangle deposition (OAD) are shown and discussed. Finally wecompare the RHEED surface pole figure technique with theconventional x-ray pole figure technique.

2. RHEED pattern analysis

2.1. Reflection and transmission patterns

RHEED patterns can be classified into reflection andtransmission patterns. For single crystal films, bothkinds of patterns are often observed, to what extentdepends on the surface morphology of the film. However,in polycrystalline films transmission patterns are usuallyobserved. The schematics of various electron scatteringgeometries, film morphologies and crystalline structures areshown in figures 1(a), (d) and (g). For a smooth single crystalsurface, electrons are reflected from the surface as shown infigure 1(a). In this reflection mode, [8, 21, 22], electrons onlypenetrate the very top atomic layers. The reciprocal space istherefore composed of a set of one-dimensional rods alongthe surface normal as shown in figure 1(b). The rods areoften broadened and have a finite width due to the existenceof either imperfections in the surface or the finite instrumentresponse of the RHEED system, or both. We can construct theEwald sphere in this reciprocal space, also shown in figure 1(b).

The intersection of the Ewald sphere with each reciprocal rodwould produce a reflected beam that is elongated into a streak.The streaks occur on the so-called Laue circles [8, 21]. Infigure 1(b) the zeroth-order Laue circle is shown as a dashedcircle. The diffraction pattern therefore consists of a series ofstreaks as shown in figure 1(c). In RHEED geometry, only theupper part of the diffraction pattern can be measured becausethe bottom part was shadowed by the substrate. The straightthrough beam is the incident electron beam without hitting thesubstrate. If one has a perfect single crystal surface and a verygood RHEED instrumental response, then the reciprocal latticerods become very narrow and the streaks shrink into spots.The corresponding diffraction pattern is indicated by dots infigure 1(c). In the reflection pattern, the specular diffractionspot labelled as (0 0) in figure 1(c) would always appear.

Although RHEED reflection patterns are mostly used byresearchers to study the properties of single crystal surface, thetransmission patterns are also often observed [8]. Figure 1(d)shows the electron incident geometry for a surface containingsmall single crystal islands. In the transmission mode, most ofthe electrons would enter the crystalline islands from one faceand are scattered out of the crystal islands through another face.Since many atomic layers parallel to the surface are involvedin the diffraction, the reciprocal space is composed of spotsas shown in figure 1(e). The corresponding diffraction patternshown in figure 1( f ) would also consist of spots. The specularspot is usually missing in the RHEED transmission pattern dueto the interference of electron scattering from different atomiclayers perpendicular to the surface. This can be used to identifywhether the RHEED image is in a reflected or a transmittedpattern. Another important feature of the transmission patternis that it is determined by the bulk of the crystals and not by theindividual faces of the crystals. In this case, the transmissionpattern can be uniquely correlated with a certain orientationof the crystals. As we will demonstrate below, this featureserves as the foundation for the study of the crystal orientationof polycrystalline films using RHEED.

Since the polycrystalline film is composed of manydifferent crystallites with different orientations, the film isusually rough, as shown in figure 1(g). In this case, theelectrons penetrate through crystallites and a transmissionelectron diffraction pattern is formed, as shown in figure 1(i).Although a single crystal can also produce transmissionpatterns, patterns from a polycrystalline film have distinctfeatures. In a polycrystalline film, all the islands have theirown crystal orientations and are not coherently related to eachother. The reciprocal space therefore is a sum of individualreciprocal spaces with different orientations [10, 11]. Whenthe crystallites are randomly oriented, the reciprocal spacestructure can be viewed as a set of concentric spheres. Infigure 1(h) we show one of these spheres as the darker sphericalimage centred at the origin of the reciprocal space or the endof �kin [10,11]. The intersection of the Ewald sphere with eachreciprocal sphere produces a circle, called the Debye ring. Thecorresponding diffraction pattern consists of concentric rings,as shown in figure 1(i). Since the incident beam passes throughthe centre of the reciprocal spheres, it is also the centre ofthe concentric rings. When a polycrystalline film develops apreferred crystalline orientation, or texture, these rings will bebroken into individual arcs as we will discuss in later analyses.

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Figure 1. The schematics of various electron scattering geometries, film morphologies and crystalline structures. (a) Single crystal filmwith smooth surface. (d) Single crystal film with islands. (g) Polycrystalline film. In (a) the electron beam is reflected from the top surfacelayer. In (d) and (g) the electron beam is transmitted through tips of islands or crystallites. �kin and �kout are the wave vectors of the incidentand scattered electron beams, respectively. The Ewald sphere constructions of electron scattering in these three cases are shown in (b), (e)and (h). Their corresponding diffraction patterns are shown in (c), ( f ) and (i), respectively. The horizontal dashed line in each of (c), ( f ) and(i) represents the shadowing edge. The straight through beam is the incident electron beam without hitting the substrate. The (0 0) in (c)represents the specular spot. The dark shaded sphere in (h) is the reciprocal structure from a polycrystalline that contains randomlyorientated crystals.

2.2. Classification of textures

Bauer categorized textures of polycrystalline films into one-degree orientation (I-O) and two-degree orientation (II-O)textures [6], which are shown in figures 2(a) and (b),respectively. I-O and II-O textures are also called fibreand biaxial textures, respectively. For the fibre texture onecrystallographic direction of the crystallites is aligned parallelto the fibre axis or the texture axis. In the azimuthal directionaround the fibre axis the crystalline orientation is randomlydistributed. See figure 2(a). If the angular orientation in theazimuthal direction is also aligned between the crystallites,then the texture is called a biaxial texture. In the biaxialtexture, two crystallographic axes point in two preferreddirections. See figure 2(b). If the crystal axes show nopreferred orientation (orientate randomly) then it is calleda random orientation. See figure 2(c). The extreme caseof a biaxial texture is a single crystal type of texture. Seefigure 2(d). All crystals axes are oriented exactly in the biaxialdirections.

2.3. RHEED patterns of textured films

RHEED patterns have been used for thin film analysis for along time [6]. However, only recently several groups startedto systematically study the RHEED patterns of textured films.For example, Stephane et al have shown how to obtain thetilt angle of a fibre texture axis and the dispersion angle of atexture axis in Fe films from RHEED patterns [10]. Dmitriet al showed a similar analysis and expanded the method to afilm having an arbitrary crystalline symmetry [11].

2.3.1. RHEED pattern from a vertical fibre texture. Ewaldsphere construction is a standard method to obtain a RHEEDpattern. For RHEED, a typical wave vector �kin is much largerthan the reciprocal lattice vector �G; therefore, the Ewald spherecan be approximated as a plane in the measurable range. Thenthe diffraction condition can be simplified as [10, 11]

�kin · �G = 0. (1)

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Figure 2. Various texture orientations in crystals: (a) I-O (fibre)texture, (b) II-O (biaxial) texture, (c) random orientation and(d) single crystal orientation. The curved double arrows in(a) and (b) indicate deviations from the preferred directions.(Reprinted with permission from [6]).

Equation (1) implies that all the reciprocal lattice vectorssatisfying the diffraction condition lie in a plane perpendicularto �kin.

For a polycrystalline film, the reciprocal space is the sumof reciprocal spaces from individual crystal grains oriented indifferent directions [10, 11]. In the case of a polycrystallinefilm without any texture or preferred crystallite alignment, thereciprocal space structure can be viewed as a set of concentricspheres, representing a random orientation. For a texturedfilm, the crystallites align around certain preferred directions;the reciprocal sphere therefore is broken into many parts.Figures 3(a) and (b) show the reciprocal space structures ofa simple cubic (sc) lattice with a (0 0 1) out-of-plane texture.For an ideal texture, i.e. when there is no deviation in thetexture orientation, the reciprocal space structure consists of aset of points along the texture direction superposed with a set ofconcentric rings lying in discrete parallel planes perpendicularto the texture direction. See figure 3(a). In the case when thereis an angular dispersion in the texture orientation, the reciprocalspace structure can be described by a set of concentric domesalong the texture direction superposed with a set of concentriccircular bands. Both domes and circular bands are parts ofconcentric spheres with a common centre at the origin of thereciprocal lattice. See figure 3(b) [11].

Assuming that the incident wave vector �kin is along the �iaxis, then the Ewald sphere can be viewed as the ( �j �k) plane. Asa consequence equation (1) implies that the RHEED diffractionis the cross section of the reciprocal space in the ( �j �k) plane.The (�i, �j , �k) is the Cartesian coordinate in the laboratoryframework where the measurement is taken. Figure 3(c)shows the calculated RHEED pattern of a (0 0 1) out-of-planetexture of a SC structure [23]. In this figure we can see thatthe pattern is basically composed of many concentric arcs,which is the signature of a polycrystalline diffraction pattern.For a particular family of crystal planes, the related arcs aredistributed in a circle having the same radius. One distinctfeature of fibre texture is that the whole pattern would besymmetrical to the texture axis, namely, the [0 0 1] texture axisin figure 3(c).

Figure 3. (a) Reciprocal space structure of a polycrystalline filmwith an ideal (0 0 1) texture in a SC lattice. The rings represent thetrajectories of reciprocal lattice points under rotation around thewell-defined [0 0 1] texture axis. (b) A sketch of the reciprocal spacestructure of a polycrystalline film with a non-ideal texture, i.e. adispersion of texture axis. The �i, �j and �k represent the bases of thelaboratory frame. (c) A calculated RHEED pattern from a (0 0 1)texture normal to the surface of a film for a SC structure. The dotnear O represents the straight through beam. (Parts (a) and (b) arereprinted with permission from [11]. Copyright 1999, AmericanInstitute of Physics.)

2.3.2. RHEED pattern of a slanted fibre texture. When thefibre axis is slanted, the entire reciprocal space would also tiltaway from the substrate normal as illustrated in figures 4(a) and(b). Figure 4(a) is the reciprocal space of an ideal tilted (0 0 1)fibre texture without any angular dispersion in the texture axis.The texture axis tilt angle β ′ is measured from the substratenormal (at a value of 54◦ in figure 4(a)). Figure 4(b) is thereciprocal space of the corresponding tilted (0 0 1) fibre texturewith an angular dispersion in the texture axis. In figure 4(c), weshow the calculated RHEED pattern of the tilted (0 0 1) fibretexture when an electron beam is along the �i axis, namely, theazimuthal angle φ = 0◦ (180◦). The azimuthal angle φ is thein-plane rotation angle measured from the �i axis. In this case,the electron beam is perpendicular to the plane determined bythe fibre axis and the substrate normal. The symmetry aboutthe surface normal in this pattern is broken. The texture tiltangle β ′ can be simply measured from the tilt angle of the(0 0 1) arc. Since the azimuthal angle around the fibre axis isfully random, this pattern contains all of the information ofcrystalline orientations. Nevertheless for this slanted texture,

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Figure 4. (a) Reciprocal space structure of a polycrystalline filmwith an ideal slanted (0 0 1) texture of a SC lattice. The texture axistilt angle β ′ = 54◦ is measured from the substrate normal. The ringsrepresent the trajectories of reciprocal lattice points under rotationaround the well-defined [0 0 1] texture axis. (b) A schematic of thereciprocal space structure of a polycrystalline film with a non-idealslanted texture, i.e. a dispersion of the texture axis. The �i, �j and �krepresent the bases of the laboratory frame. The azimuthal angle φ

is the in-plane rotation angle measured from the �i axis. (c) Acalculated RHEED pattern from the slanted (0 0 1) texture for a SCstructure, when φ = 0◦ (180◦) or along the �i axis. In this case, theelectron beam is perpendicular to the plane determined by the fibreaxis and substrate normal. The dot near O represents the straightthrough beam. (d) The diffraction pattern when the electron beam isalong the �j axis, namely φ = 90◦ (270◦). (Parts (a) and (b) aremodified schematics from [11]. Copyright 1999, American Instituteof Physics.)

the diffraction pattern would look dramatically different whenthe electron beam is incident at different azimuthal angles φ.The angle φ is the in-plane rotation angle measured from the�i axis. Figure 4(d) shows the diffraction pattern when theelectron beam is along the �j axis, namely, φ = 90◦ (270◦).We can see that the pattern is symmetric with respect to thesubstrate normal and the slanted nature of texture cannot beobserved directly.

Although diffraction patterns have often been used fortexture analysis, it can become much more complicated

when multiple textures exist or when the texture is weak[16, 19]. For a biaxial texture, due to the confinement ofthe azimuthal angle orientation, the diffraction patterns willbe always different when the electron beam is incident atdifferent azimuthal angles. From a single diffraction pattern itis difficult to obtain quantitative information on the azimuthalangle orientation. To determine a biaxial texture, especiallythe azmithal orientation, a collection of multiple diffractionpatterns is normally required. Brewer et al [18] have used aRHEED in-plane rocking curve to obtain the information onthe azimuthal angle orientation. In the following section, wewill demonstrate our newly developed RHEED surface polefigure technique [19, 20].

3. RHEED surface pole figure construction

3.1. Experimental RHEED setup for surface pole figuremeasurements

Figure 5(a) shows a schematic of the experimental setup forthe RHEED surface pole figure measurement in an ultrahighvacuum chamber [19, 20]. In our RHEED experiments, theelectron gun was typically operated at 9 kV. RHEED patternson a phosphor screen were recorded using a charge-coupleddevice (CCD). As we will show later, from a single RHEEDpattern, we are able to obtain a slice of the pole figure. Thisslice is the pole density along different polar angles θ at a fixedazimuthal angle φ. A UHV step motor is used to rotate thesubstrate in-plane to obtain different slices of the pole figure.The sample holder is adjustable so that the substrate normal canbe almost exactly aligned along the rotational axis of the stepmotor. In this case the wobbling of the substrate is minimizedto less than 0.05◦. The step motor has a step size of 1.8◦. Atotal of 200 patterns covering the azimuthal angle of 360◦ wasrecorded for the pole figure measurements. The exposure timefor each image was 5 s. The total data collection time was∼20 min. For in situ characterization an evaporation sourcewas added in the UHV chamber, as shown in figure 5(a) [16].The evaporation source can move along a semi-circular trackallowing the deposition angle to be varied.

3.2. Construction of RHEED surface pole figure using a 2Ddetector

In RHEED we use a phosphor screen as a two-dimensionaldetector to collect diffraction patterns. The use of atwo-dimensional area detector to construct pole figureshas been reported in XRD [24–27] and in transmissionelectron microscopy (TEM) operated in both transmission andreflection modes [28]. Compared with a point detector, thetwo-dimensional detector can collect a large range of polarangles at each azimuthal angle. This would tremendouslyreduce the data collection time.

Figure 5(b) shows a schematic to demonstrate the principleof using a two-dimensional detector to construct a pole figure.The grey sphere in figure 5(b) represents the reciprocal space ofa family of crystal planes, for example, the (hkl) plane.The film is assumed to have a random orientation. In themeasurement, the Bragg diffraction for the (hkl) plane can onlybe satisfied when the amplitude of the difference between �kin

and �kout is equal to the radius of the (hkl) reciprocal sphere.

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Figure 5. (a) A schematic of the experimental setup for RHEEDsurface pole figure. A UHV step motor is used to rotate the substratein-plane to obtain different slices of the pole figure. The angle φ isthe azimuthal angle around the substrate normal. The angle θ is thepolar angle measured from the substrate normal. For in situcharacterization an evaporation source was added in the UHVchamber, as shown in (a). The evaporation source can move along asemi-circular track allowing the deposition angles to be varied. (b)A schematic to demonstrate the principle of using two-dimensionaldetector to construct a pole figure. �kin and �kout are the wave vectorsof incident and scattered electron beams, respectively. The greysphere in (b) represents the reciprocal space of a family of (hkl)crystal plane. The specific Bragg angle is 2θ(hkl). For a particularkin, the points satisfying the (hkl) Bragg diffractions are distributedalong a bolded circle shown in (b). (c) demonstrates the relationshipbetween a diffraction pattern and a pole figure. The bolded straightline in (c) is the projection of a (hkl) diffraction ring.

Then the angle between �kin and �kout is equal to the specificBragg angle 2θ(hkl). For a particular �kin, these points aredistributed along a bold circle or Debye ring. From the figure,we can see that this circle almost covers the full range of thepolar angle θ , from 0◦ to 90◦, at a fixed azimuthal angle φ.Using a two-dimensional detector, it is possible to record thewhole (hkl) diffraction ring, shown in figure 5(a), to constructthe (hkl) pole figure. Then the substrate just needs to be rotatedazimuthally in order to record the diffraction intensities atvarious space orientations. In the RHEED measurement, thescattered electron beam is confined in a small spatial angle, sothe whole diffraction ring can be easily captured. However,for XRD, x-rays can be scattered into much larger spatialangles so that a 2D detector may not be able to cover thewhole range of a particular Bragg scattering. Figure 5(c)demonstrates the relationship between a diffraction pattern anda pole figure. By definition a pole figure is a stereographicprojection that represents the variation of the pole densitydistribution of a specific family of planes [7]. If one projectsthe (hkl) diffraction ring in figure 5(b) to the equator planehighlighted by the dashed circle then this would correspondto a slice of the corresponding (hkl) pole figure. This slice isrepresented as the bold straight line in figure 5(c). If the filmdoes not have a random orientation but has a texture then the

continuous ring will be broken into arcs and the projection ofarcs will have discrete poles or a variation of the pole densitydistribution. As the substrate is rotated azimuthally, differentslices can be obtained to make up the whole pole figure.

4. Examples of RHEED surface pole figureconstruction

4.1. Fibre texture in vertical Ru nanorods

To illustrate the basic process of constructing a surface polefigure through RHEED images, we use a film with vertical Runanorods (∼340 nm thick) as an example [19]. Figure 6(a) isan scanning electron microscopy (SEM) cross section of theRu film. The Ru vertical nanorods were formed by obliqueangle sputter deposition with substrate rotation. Under OAD,the flux reaches the substrate at an angle tilted away fromthe substrate normal while the substrate is rotating around thesubstrate normal [29–33]. The shadowing effect in OAD leadsto the nanostructured film. This growth method has provideda simple and versatile means of producing three-dimensionalnanostructures from a wide variety of materials.

Figure 6(b) shows a typical ex situ RHEED diffractionpattern. The absence of a specular reflection spot indicatesthat this is a transmission pattern. The image consists ofmany diffraction arcs from different families of crystal planes.Before delving into the construction of a pole figure fromthe RHEED patterns, we discuss two generic features in thetransmission patterns which may affect our measurements:Kikuchi lines and electron refraction effects [2,8]. A Kikuchiline is a typical feature found in the transmission patterns ofa thin single crystal film [8]. The Kikuchi lines originatefrom electrons that are inelastically scattered. These linesare distributed in places associated with the particular singlecrystal orientation and the direction of the incident electronbeam. In a polycrystalline film, the Kikuchi lines from a largenumber of differently oriented crystallites will overlap. Thesemay result in a uniform background and without resolvablelines from any particular crystallite, as shown in figure 6(b).This background can be subtracted as we will discuss later inour analyses.

Another feature usually found in transmission patterns isthe electron refraction effect due to the inner potential of thecrystal. The refraction effect is most obvious when the electronbeam passes through the boundaries of the crystallites, whichleads to a shift of the diffraction arc. We have previouslyobserved a splitting up to 2.1% of the radius of the Cu (2 2 0)diffraction arc [16]. In the case of Ru, we did not observeobvious splitting, as shown in figure 6(b). This may be due tothe fact that the intensity from the refracted electron is weak,which causes a broadening of the diffraction arcs instead ofdistinct splitting arcs. In figure 6(b), the ratios between thevarious radii of the Ru diffraction rings match with a perfectHCP structure [17]. This indicates that the refraction effectis weak. In the pole figure construction, we integrate theintensity across the diffraction ring that will actually includecontributions from both the unrefracted and refracted electrons.

For a particular family of crystal planes, such as (1 0 1 1)labelled in figure 6(b), the related arcs are distributed in acircle having the same radius. The polar angle θ is defined

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Figure 6. (a) A SEM cross-sectional view of a Ru film with verticalnanorods (∼340 nm thick). The scale bar is 100 nm. (b) An ex situRHEED pattern from the film with vertical Ru nanorods (∼340 nm).The polar angle θ is the angle measured from the substrate normal.(c) The normalized intensity profile of a slice from the (1 0 1 0) polefigure (filled squares) and the normalized intensity profile of a slicefrom the (1 0 1 1) pole figure (open squares) at φ = 0◦ (180◦). Theangle φ is the azimuthal angle around the substrate normal.

by the angle tilting away from the substrate normal. Withoutsignificant distortion of images, the maximum polar angleθ that can be reached is ∼70◦ due to the shadowing of thesubstrate. The intensity distribution along a particular ringas a function of θ represents one ‘slice’ of the pole figurefor a particular azimuthal (in-plane) angle φ. Figure 6(c)shows the normalized intensity profile of a slice from the(1 0 1 1) pole figure (open squares) and the normalized intensityprofile of a slice from the (1 0 1 0) pole figure (filled squares)

at φ = 0◦ (or equivalent to 180◦). The procedure fornormalization of the intensity is as follows. To obtain theintensity of a θ value from the diffraction ring, which is usedfor constructing a pole figure, we first integrate the intensityacross that ring at the corresponding polar angle θ . Thediffraction patterns usually have a diffuse background due tomultiple and inelastic scatterings. Therefore, after integratingthe intensity the background is subtracted. Next, the intensity,after the background subtraction, is normalized by dividing thebackground intensity. The last step is necessary because theintensity attenuation due to the multiple scattering depends onthe distance from the shadow edge [15]. The value used forthe background division normally is taken to be the intensityof the point slightly to the outside of the ring at the same polarangle θ .

The sample is then rotated around the surface normalto a different azimuthal angle φ in order to take anotherdiffraction pattern. Another slice of pole figure is then obtainedby measuring the intensity distribution along the ring withthe same radius. The whole pole figure is then constructedby combining different ‘slices’ at various azimuthal anglesranging from 0 to 360◦. During the construction, the curvatureof the Ewald sphere is also considered. However, its effectson the pole figure analysis are negligible [10, 11]. Figure 7(a)shows that the contour plot of the constructed (1 0 1 1) polefigure from these intensity profiles illustrates the azimuthalsymmetry of the vertical Ru rods well. Similarly figure 7(b)shows the (1 0 1 0) pole. The solid black rings shown in thefigure are the calculated intensity distributions of the (1 0 1 1)pole figure assuming a perfect (1 0 1 0) fibre texture.

4.2. In situ RHEED surface pole figure of biaxial textureevolution in Mg nanoblades

A similar pole figure construction process for a fibre texturecan also be applied to a film with a biaxial texture. Thedevelopment of biaxial texture has attracted significant interestin many areas [34–38] since the biaxial texture mimicsthe orientation of a single crystal. For example [35],high temperature superconducting copper oxides have beendeposited on MgO biaxial films to minimize high angle grainboundaries. A much higher current density can be achievedwith the superconducting layer deposited on the biaxial film.There are several evaporation methods that produce biaxiallytextured films, such as ion beam assisted deposition (IBAD)and OAD. Due to the simplicity and low cost, OAD has beenrecognized as an effective way to control the thin film texture.Biaxial texture is often observed under OAD with a stationarysubstrate. The oblique incident vapour flux breaks not onlythe azimuthal symmetry of crystal orientation but also theazimuthal symmetry of film morphology. This morphologicalanisotropy can severely distort the constructed pole figures.Here we used a very anisotropic Mg film as an example. Thisfilm was grown by OAD and composed of many ultrathinnanoblades [39]. We show that an extra intensity normalizationprocess has to be used to compensate for the effects of filmmorphology in the construction of the RHEED pole figure. Wewill also apply an in situ RHEED surface pole figure techniqueto investigate the texture evolution of the Mg film grown underOAD. For in situ characterization a Mg evaporation source

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Figure 7. The contour plots of a constructed (a) (1 0 1 0) pole figureand (b) a (1 0 1 1) pole figure from RHEED measurements of Ruvertical nanorods. The solid black rings shown in the figures arecalculated intensity distributions of the (1 0 1 0) and (1 0 1 1) polefigures assuming a perfect (1 0 1 0) fibre texture.

was added to the UHV chamber, as shown in figure 5(a). Theevaporation source can move along a semi-circular track toadjust the vapour deposition angle.

The substrate used for deposition was a Si wafer with a thinlayer of native oxide on the surface. The vapour incident anglewith respect to the substrate normal is ∼75◦. The distancebetween the evaporation source and the substrate holder wasapproximately 10 cm. The source was resistively heated toa desired temperature of ∼600 K for evaporation. The basepressure of the vacuum chamber was ∼4 × 10−9 Torr. Duringthe deposition the pressure rose to ∼2.0 × 10−8 Torr. The Mgdeposition was interrupted at 0.5, 4.5, 8.5, 13.7, 24.5, 34.7and 49.7 min for in situ RHEED pole figure measurements.The morphologies and structures of the final Mg films wereimaged ex situ by a field emission SEM. The thickness of thefinal Mg film obtained from the cross-sectional SEM images is∼2.1 µm. The thickness refers to the vertical distance betweenthe substrate and the Mg film surface. The growth rate wasdetermined to be ∼43 nm min−1.

4.2.1. Anisotropic morphology and azimuthal angle dependentRHEED patterns. Due to the very fast diffusion of Mg atoms,during OAD the Mg film growth deviated significantly fromthe past experimental results for other materials using OADand theoretical predictions [39]. Figures 8(a) and (c) showSEM top view images of the final Mg film deposited for49.7 min (∼2.1 µm thick) at a vapour incident angle of 75◦.From the top views, we can see that the film is composedof many nanoblades. These nanoblades are well aligned.

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Figure 8. (a) and (c) The SEM top view images of the final Mgnanoblade film deposited for 49.7 min (∼2.1 µm thick) at a vapourincident angle of ∼75◦. The geometry of RHEED measurement atthe azimuthal angle φ = 0◦ (180◦) is shown in (a). The angle φ isthe azimuthal angle around the substrate normal. The azimuthalangle φ = 0◦ (180◦) is defined when the direction of the incidentelectron beam is 90◦ with respect to the flux direction. In thisgeometry the electron beam direction is parallel to the wider widthdirection of nanoblades. (c) The geometry of the RHEEDmeasurement at the azimuthal angle φ = 90◦ (270◦), when the widerwidth direction of nanoblades is perpendicular to the electron beamdirection. The RHEED patterns recorded at φ = 0◦ (180◦) andφ = 90◦ (270◦) are shown in (b) and (d), respectively.

This suggests that the Mg nanoblades have two preferredcrystalline orientations, namely, biaxial or II-O texture. In abiaxial texture, due to the confinement of the azimuthal angleorientation the diffraction patterns will be different when anelectron beam is incident at different azimuthal angles.

In the RHEED pole figure measurement, the substrate isrotated azimuthally at an angle φ around the substrate normal.The geometry of the RHEED measurement at the azimuthalangle φ = 0◦ (180◦) is shown in figure 8(a), where we definedthe azimuthal angle φ = 0◦ (180◦) when the direction ofthe incident electron beam is 90◦ with respect to the fluxdirection. In this geometry the electron beam direction isparallel to the wider width direction of nanoblades. Figure 8(b)is the RHEED pattern for the 49.7 min deposited film when thesubstrate is positioned at φ = 0◦ (180◦). The diffraction ringsare sharper and break into arcs which indicate the formation oftexture. Lower order arcs are labelled as (1 0 1 0) and (1 0 1 1).The pattern is asymmetric about the substrate normal. Thisasymmetry is a result of the oblique angle incident vapourdeposition. As the substrate is rotated, the φ angle changeswith respect to the incident electron beam direction. This alsomeans that the wider width direction of nanoblades is rotatedwith respect to the electron beam direction. When the substrateis rotated to φ = 90◦ (270◦), the wider width direction ofnanoblades is perpendicular to the electron beam direction.

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Figure 8(c) is the geometry of the RHEED measurement atthe azimuthal angle of φ = 90◦ (270◦). The correspondingRHEED pattern is shown in figure 8(d) and is symmetric.Figures 8(b) and (d) indicate a strong azimuthal dependentRHEED pattern for the nanostructures grown by OAD.

4.2.2. Normalization of RHEED surface pole figure ofnanostructures with anisotropic morphology. From the topview SEM images shown in figure 8(a), we can see that themorphology of the Mg film is extremely anisotropic. Thisanisotropic morphology can severely distort the RHEED polefigure, which is constructed from the polar intensity profilesat different azimuthal angles. In this section, a methodof intensity normalization is presented to take care of thisgeometrical effect. For RHEED, a typical wave vector ofincident electron beam �kin is much larger than the interestedreciprocal lattice vector G; therefore, the Ewald sphere couldbe approximated as a plane. Figure 9(a) shows a 3D diagram ofthe constructed reciprocal space from the RHEED patterns ofthe Mg film deposited at 49.7 min (∼2.1 µm thick). Under theassumption that the Ewald sphere is approximated as a plane,the RHEED patterns at different azimuthal angles will have acommon intersection line along the substrate normal, namely,the Sk axis. In particular, point A on the Sk axis is the crosspoint between the (1 0 1 0) arcs. Theoretically the intensity ofpoint A obtained from RHEED patterns at different azimuthalangles should have the same intensity. However, fromfigure 9(b), we can see that this intensity shown as filled squaresvaried significantly with respect to the azimuthal angles. Thevalley of the intensity plot is around φ = 0◦ (180◦) while thepeak intensity is around φ = 90◦ (270◦). Similarly for crosspoint B between (1 0 1 1) arcs the intensity (open squares) alsovaries with the azimuthal angle as shown in figure 9(b). Weargue that this intensity modulation in the azimuthal anglesis due to the anisotropic morphology of the film. From theSEM image we can see that the film is composed of well-aligned nanoblades with wider surface (face) perpendicularto the vapour flux. During the measurement, when anelectron beam is incident parallel to the wider width directionof nanoblades, shown in figure 8(a) for the measurementgeometry, gaps between the nanoblade rows are exposed tothe incident electrons that allow more electron channellinginto the depth of the material. The channelled electrons willbe captured in the bulk or contribute to the background [8],which results in a weaker intensity at φ = 0◦ (180◦). Theeffect of electron channelling has been discussed in detail byBraun [8]. However, when the electron beam is perpendicularto the wider surface of nanoblades, shown in figure 8(c) forthe measurement geometry for φ = 90◦ (270◦), the electronsare incident perpendicular to the channelling gaps and thediffraction intensity becomes strongest. Both arguments areconsistent with the observations presented in figure 9(b).

To compensate for the intensity modulation around theazimuthal angles, shown in figure 9(b), we normalize theintensity of point A in different RHEED images to a constantvalue. In figures 10(a) and (b) the (1 0 1 0) RHEED polefigures of the film deposited at 49.7 min before and afternormalization are shown. The intensity around φ = 0◦

(180◦) indicated by the dashed line was basically obtainedfrom RHEED images when the electron beam was incident

100500 150 200 250 300 3500.60.81.01.21.41.61.82.02.22.42.62.83.03.23.43.6

Modulation of azimuthal intensity around θ = 0° at A Modulation of azimuthal intensity around θ = 0° at B

Inte

nsity

(ar

b. u

nits

)

Azimuthal angle φ(b)

(a)

Figure 9. (a) A 3D construction of the reciprocal space from theRHEED patterns of the Mg nanoblade film deposited for 49.7 min(∼2.1 µm thick). The points A and B on the Sk axis are the crosspoints of the (1 0 1 0) arcs and (1 0 1 1) arcs, respectively. The polarangle θ is measured from the substrate normal, namely, the Sk axis.The angle φ is the azimuthal angle around the substrate normal. (b)The plots of the intensity at point A (filled squares) and point B(open squares) versus the azimuthal angle φ.

parallel to the wider surface of the nanoblades. Beforenormalization, this intensity was significantly lower than thesurroundings due to the intensity modulation described above.After normalization a centre pole clearly showed up along thedashed line. The pole structure suggests the formation of thebiaxial texture. Through the analyses of the angles betweendifferent diffraction poles, [19, 20] we found the formation ofa (1 0 1 0)[0 0 0 1] biaxial texture in the Mg nanoblade film.The calculated positions of the diffraction intensity for thisbiaxial texture were superimposed on the top of figure 10(b) assolid squares. A similar normalization process is also followedby the construction of other pole figures. Figures 10(c) and(d) show the (1 0 1 1) RHEED pole figures before and afterthe normalization, respectively. After normalization, the splitcentre poles shown in figure 10(c) are merged into a single poleshown in figure 10(d). The positions of the individual polesmatch the theoretical positions of a (1 0 1 0)[0 0 0 1] biaxialtexture very well.

4.2.3. Evolution of texture in Mg nanoblades from normalizedRHEED pole figures. Figure 11 shows normalized (1 0 1 0)and (1 0 1 1) RHEED pole figures at 8.5 (∼365 nm thick),24.5 min (∼1.05 µm thick) and 34.7 min (∼1.49 µm thick)depositions. In the beginning of the 0.5 min deposition thedistribution of the intensity in the pole figure is nearly even

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Figure 10. The (1 0 1 0) RHEED surface pole figures of the Mgnanoblade film with a deposition time of ∼49.7 min (a) beforeintensity normalization and (b) after intensity normalization; (c) and(d) show the corresponding (1 0 1 1) RHEED pole figures before andafter intensity normalization. The dashed line represents theazimuthal positions, where φ = 0◦(180◦).

(not shown here), which indicates a random initial nucleationon the amorphous substrate. With more deposition at 8.5 min,an intense band is shown on the left side of the pole figuresin figures 11(a) and (b). Clearly separated poles are revealedin the longer deposition times of 24.5 min (∼1.05 µm thick)and 34.7 min (∼1.49 µm thick). The position of the poles inthe figures moves towards the flux as the film grows. Thisindicates that the texture axes tilts more towards the flux. Thischange in the texture axis can be quantitatively characterizedby the evolution of polar intensity profiles, measured fromRHEED images at φ = 0◦ (180◦) [20]. In addition to themovement of the pole position, we can also see that (1 1 0 1),(1 0 1 1) and (0 1 1 1) poles lie on a circular band shown as thedashed curve in figure 11(f ). The centre of the circle is thegeometrical position of the [0 0 0 1] axis. This circular bandindicates that the variation of the azimuthal angle orientationis mainly around the [0 0 0 1] axis. This rich information onthe texture evolution cannot be obtained from the x-ray polefigure technique.

5. A comparison between RHEED surface polefigure and x-ray pole figure using area detector

The x-ray pole figure technique has been well establishedand widely applied to characterize the texture of thin films.However, XRD probes the average texture of the entirethickness of the film as the x-ray penetrates through the entirefilm (a few micrometres thick). Therefore, the x-ray pole figureis not suitable to study the surface texture evolution of a film. Inthis section, we give an example that compares the x-ray pole

Figure 11. The normalized (1 0 1 0) RHEED surface pole figures atdeposition times (a) 8.5 min (∼365 nm thick), (c) 24.5 min(∼1.05 µm thick) and (e) 34.7 min (∼1.49 µm thick). Thenormalized (1 0 1 1) RHEED surface pole figures at correspondingdeposition times are shown in (b), (d) and (f ). The positions ofpoles in the figures move towards the incident vapour flux (directionindicated in (b)) as the film grows. The intensity of the azimuthalplot is around the white dashed circle which goes through (1 1 0 1),(1 0 1 1) and (0 1 1 1) poles, as shown in (f ). The centre of the circleis the geometrical position of the [0 0 0 1] axis.

figure and the RHEED surface pole figure taken with differentthicknesses of Mg nanoblades which demonstrates this pointclearly.

Before we compare the RHEED surface pole figure withthe x-ray pole figure analysis we briefly describe the x-raypole figure technique. In the conventional x-ray pole figuresetup, one uses a point detector to collect the diffractionintensity. To construct a pole figure, intensities at thousandsof different spatial angles in θ and φ have to be measured.Construction of one pole figure could take considerable amountof time. Recently the technology of the x-ray area detector hasbeen greatly advanced. The commercial availability of 2D x-ray detectors has made their high speed acquisition available[24–27]. Figure 12(a) shows a schematic of the x-ray polefigure setup using an area detector. In the setup the x-raysource and detector are fixed while the sample can be rotatedazimuthally in angle φ and tilted at different χ angles. Thex-ray is usually scattered into a large spatial angle so thatthe x-ray area detector may not be able to cover the wholerange of a particular Bragg diffraction ring, as demonstrated in

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Figure 12. (a) A schematic of the x-ray pole figure setup using anarea detector. In the setup the x-ray source and detector are fixedwhile the sample can be rotated azimuthally in an angle φ and tiltedat different χ angles. When the x-ray detector cannot cover thewhole range of a particular Bragg diffraction ring represented by abold circle, the tilting of the sample is necessary to construct acomplete pole figure. �kin and �kout are the wave vectors of theincident and scattered x-ray beams, respectively. The 2θBragg is thediffraction angle for the particular diffraction ring. (b) A schematicof the Ewald sphere construction (light shaded sphere) in XRD anda reciprocal space structure of randomly oriented crystals (darkershaded sphere). The horizontal dashed line represents theshadowing edge. The finite size area detector in (a) catches part ofthe intensity ring below the shadow edge in (b).

figure 12(a). In this case, the tilting of the sample is necessaryto construct a complete x-ray pole figure. The constructionof a pole figure using an x-ray area detector from multiplediffraction patterns is similar to the construction of the RHEEDsurface pole figure. However, in a typical XRD measurement,the radius of the Ewald sphere is much smaller than that of theRHEED diffraction. For example, the typical electron energywe used in our RHEED is 9 KeV, which gives a wave vector of∼48 Å−1. This value is much larger than the wave vector for aCu Kα x-ray, which is ∼4 Å−1. The x-ray Ewald sphere shownin figure 12(b) as a light shaded region cannot be approximatedas a plane as illustrated in the schematic of figure 1(h). Thedarker shaded sphere centred at the origin of the reciprocalspace or the end of �kin is the reciprocal space structure from apolycrystalline sample. The measured diffraction ring froma polycrystalline sample also tilts away significantly fromthe substrate normal (perpendicular to the horizontal dashedline that is the shadow edge in figure 12(b)) when the x-rayis not incident from a grazing angle. In this case a morecomplex geometrical conversion, connecting the diffractionpattern to the spherical cutting of the x-ray Ewald sphere, hasto be used to construct a pole figure [24]. This conversionrelationship depends on the crystal structure, the wavelengthused and the size and the position of the detector [24]. Sincethe distance between a particular point on the diffractionpattern and the sample can vary significantly, the measureddiffraction intensity also needs to be normalized by dividing

Figure 13. A comparison between the x-ray pole figures andRHEED surface pole figures of 2.1 and 12 µm thick Mg nanobladefilms. The (1 0 1 0) and (1 0 1 1) x-ray pole figures: (a) and (b) for2.1 µm thickness; (e) and (f ) for 12 µm thickness. The whole x-raypole figure was composed of by stitching three parts that are from∼0◦ to ∼30◦, ∼30◦ to ∼60◦ and ∼60◦ to ∼80◦. The white dashedcircles in (a) illustrate the stitching locations. The (1 0 1 0) and(1 0 1 1) RHEED surface pole figures: (c) and (d) for 2.1 µmthickness; (g) and (h) for 12 µm thickness.

the square of that distance [24]. In addition, most of the Braggdiffractions corresponding to large reciprocal space vectorswould be absent in the XRD patterns [24, 27]. In contrast, theEwald sphere of RHEED at an in-plane azimuthal angle can beapproximately viewed as a plane; therefore RHEED patternscan cover almost half of the reciprocal space if one rotates thesubstrate.

Figures 13(a)–(h) show a comparison between the x-raypole figures and the RHEED surface pole figures of 2.1 and12 µm thick Mg nanoblades. The x-ray pole figures were takenusing a Bruker D8 Discover diffractometer. The primary Cux-ray wavelength is Kα at 1.5405 Å. The detector was placed at

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Table 1. A comparison between the RHEED surface pole figure and the x-ray pole figure.

RHEED surface pole figure X-ray pole figure

Sample tilt mechanism Not needed Usually neededData collection speed Fast SlowEwald sphere Nearly a plane Small radius of k

(large radius of k)Probing depth Nanometres MicrometresScattering cross section Strong WeakMultiple scattering Strong WeakStatistics Near film surface Average of the entire filmIn situ study Yes ChallengingSubstrate interference None for film thicker than Substrate poles may appear

a few nanometres together with thin film polesMaterials type Conducting and semiconducting solids Conducting, semiconducting,

and non-conducting solids,fluids, polymers, etc

15 cm from the sample yielding a polar angle coverage of∼33◦.Due to the limited detector size, only part of the diffractionpattern is covered. For obtaining a full pole figure, the sampleis tilted at three different angles χ : 12◦, 42◦ and 72◦. At eachangle the sample was rotated through an φ angle of 360◦ at 8◦,5◦ and 5◦ step sizes for the respective tilts.

Figure 13(a) is the (1 0 1 0) x-ray pole figure for the2.1 µm thick Mg nanoblades. The whole pole figure wasmade up by stitching three parts that are from ∼0◦ to ∼30◦,∼30◦ to ∼60◦ and ∼60◦ to ∼80◦. The white dashed circlesin figure 13(a) indicate the stitching locations. These partscorrespond to the tilting of the sample at 12◦, 42◦ and 72◦,respectively. Since the detector covered a range of polarangles of ∼33◦, each respective tilt measured the polar angleranging from ∼0◦ to ∼28.5◦, ∼25.5◦ to ∼58.5◦ and ∼55.5◦

to ∼88.5◦. Between each set of patterns, there was a narrowrange of polar angles overlapped. The stitching was simplyperformed by assuming that the overlapped angles have thesame intensity. Figure 13(b) is the (1 0 1 1) x-ray pole figure forthe 2.1 µm thick Mg nanoblades. Both these pole figures showthe intensity variation, but no distinct pole structures are clearlyresolved. In contrast, the RHEED surface pole figures for thisfilm thickness shown in figures 13(c) and (d) revealed clearpoles, which indicates the formation of a strong surface biaxialtexture. Our previous RHEED pole figure analysis showed thatthe biaxial texture changed continuously in the early growthstage. Since x-ray pole figures measure the average texture ofthe entire film, it is not surprising to observe the absence ofdistinct poles in the x-ray pole figures. For a thinner film thestrong electron scattering cross section also provides a bettercontrast in the RHEED surface pole figure.

For the 12 µm thicker Mg nanoblades the intensitycontrast in the x-ray pole figure in figures 13(e) and (f )improved compared with that of the 2.1 µm thick film shownin figures 13(a) and (b). The intensity associated with the(1 1 0 0), (1 0 1 0) and (0 1 1 0) poles in figure 13(e) are muchmore obvious and defined, so is the intensity associated withthe poles in figure 13(f ). For this thicker film, the x-ray polefigures resemble the RHEED surface pole figures, shown infigures 13(g) and (h). This indicates that the texture has beenstabilized in the latter growth stage of the Mg films, so theaverage texture of the film within the probing depth of the x-rayis similar to that of the surface texture. In reality during growththe texture shown by RHEED surface poles in figures 13(c)

and (d) for 2.1 µm thick film continued to evolve as the filmbecomes thicker. This is clearly seen from the 12 µm thick filmthat three surface poles moved towards the centre as shown infigures 13(g) and (h).

From the above example we clearly demonstrate thesurface sensitive nature of the RHEED surface pole figurecompared with that of the conventional x-ray pole figure. Thismakes RHEED a very powerful tool for in situ characterizationand motoring of thin film texture evolution. In addition, anypoles from the substrate would not appear in the RHEEDsurface pole figure because of limited electron penetrationdepth even when the film is very thin. This is not the case forthe x-ray pole figure where the poles from the substrate oftenappear due to the large x-ray penetration depth. In table 1, wesummarize the comparison between the RHEED surface polefigure and the x-ray pole figure techniques.

6. Conclusions/remarks

In summary, we showed that it is possible to construct areflection high-energy electron diffraction (RHEED) surfacepole figure of a polycrystalline film by recording multipleRHEED patterns as we rotate the substrate around the surfacenormal. Since electrons have limited penetration depth, thepole figure constructed is a surface pole figure. It is incontrast to the conventional x-ray pole figure which givesthe average texture information of the entire film. Ruvertical nanorods and Mg nanoblades are used as examplesto demonstrate the pole figure construction processes of afibre and a biaxial texture, respectively. For a biaxiallytextured film, the film morphology often has an in-planeanisotropy. This morphological anisotropy could severelydistort the constructed pole figures, as shown in our in situ studyof Mg nanoblades growth. To compensate for the effects ofanisotropic morphology in the RHEED pole figure, additionalintensity normalization has to be applied. A more detailedcalculation of the orientation density function (ODF) of thepole figures can be carried out [7, 40]. The ODF basicallyis the volume fraction of all crystallites with a particularorientation. Thus allows a quantitative description of thetexture of a crystalline phase. Armed with the RHEEDsurface pole technique, one would be able to study how thetexture changes during different stages of growth and to gaininsights into factors that control the texture formation through

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atomistic models. Experimentally further improvements indata collection and RHEED pole figure construction can bedone. For example, it would be desirable to put an energy filterin front of the phosphor screen to reduce the contribution of thebackground intensity originating from the inelastic scattering.Also in order to reduce the overlapping of adjacent diffractionrings, a lower energy (less than 9 KeV) electron beam can beused to increase the angular separation between the rings.

Acknowledgments

FT was supported by the NSF NIRT award 0506738 and TP wassupported by the DOE (education) GAANN P200A030054.The authors Dr Sabrina Lee for her help in x-ray pole figuremeasurements.

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